Tuning magnetic order with geometry: Thermalization and defects in two-dimensional artificial spin ices
Gavin M. Macauley, Gary W. Paterson, Yue Li, Rair Macêdo, S. McVitie, R. L. Stamps
Abstract
Artificial spin ices are arrays of correlated nanoscale magnetic islands that prove an excellent playground in which to study the role of topology in critical phenomena. Here, we investigate a continuum of spin ice geometries, parametrized by rotation of the islands. In doing so, we morph from the classic square ice to the recently studied pinwheel geometry, with the rotation angle acting as a proxy for controlling interisland interactions. We experimentally observe a transition from antiferromagnetic ordering in square ice to a slight preference for ferromagnetic vertices in the weakly coupled pinwheel ice using Lorentz transmission electron microscopy on thermally annealed cobalt arrays. The rotation angle also affects the relaxation timescales for individual arrays, leading to varying degrees of thermalization, and an apparent change in the nature of the defects supported: from one-dimensional strings in square ice to two-dimensional vortexlike structures for geometries similar to pinwheel. The numerical scaling of these quantities is consistent with that predicted by the Kibble-Zurek mechanism. Our results show how magnetic order in artificial spin ices can be tuned by changes in geometry and suggest the possibility of realizing a truly frustrated ice-rule phase in two-dimensional systems. Furthermore, we demonstrate this system as a test bed to investigate out-of-equilibrium dynamics across phases.